Question

1. Costs are rising for all kinds of health care. The mean monthly rent at assisted-living facilities was recently reported to have increased 18% over the last five years. A recent random sample of 121 observations reported a sample mean of $3486. Assume that past studies have informed us that the population standard deviation is $650. For this problem, round your answers to 2 digits after the decimal point.

(a) What are the end points of a 90% confidence-interval estimate for the mean monthly rent in the population? [ , ]

(b) What are the end points of a 95% confidence-interval estimate for the mean monthly rent in the population? [ , ]

(c) What are the end points of a 99% confidence-interval estimate for the mean monthly rent in the population? [ , ]

2. Sometimes we do not want one of the usual confidence levels. What is zα/2 , when the confidence level is 43.8%? For this problem, round your answers to 3 digits after the decimal point.

3. Customer satisfaction is measured on a scale between -2 and 2. The last survey estimated mean customer satisfaction to be .5700000000000001 with a known standard deviation of 4.28. Another survey is going to be taken. Given past results, you really need to have a margin of error of .19 in your 95% confidence interval. What is the smallest sample size that will get you this margin of error? 4. Sometimes we want a confidence level using the t distribution What is tα/2 , when there are 16 degrees of freedom and the confidence level is 98%? For this problem, round your answers to 3 digits after the decimal point. 1 5. The U.S Census has estimated the percentages of the U.S population that have achieved different levels of education. See https://factfinder.census.gov/faces/tableservices/jsf/ pages/productview.xhtml?src=CF for some of the estimates. This question uses numbers inspired by these results. Suppose that the sample proportion for the U.S. population aged between 25 and 34 years that has a Bachelors’s degree or higher is .35. Further suppose that this estimate came from a survery of 1393 people. (a) What are the end points of a 90% confidence interval estimate for the population proportion? (Round to 2 digits after the decimal place.) [ , ] (b) What are the end points of a 95% confidence interval estimate for the population proportion? (Round to 2 digits after the decimal place.) [ , ] (c) What are the end points of a 99% confidence interval estimate for the population proportion? (Round to 2 digits after the decimal place.) [ , ] 6. The American Time-Use Survey uses surveys to estimate how much time people in the U.S. spend doing various activities. See https://www.bls.gov/news.release/pdf/atus.pdf for some recent estimates. The numbers in this question are inspired by these results. We want to know the mean number of hours worked on a weekend day, among those who work weekends. Suppose that a simple random sample of size 1181 from the target population produced a sample mean of 5.3 hours. Further suppose that the sample standard deviation was 1.9. (a) What are the end points of a 90% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.) [ , ] (b) What are the end points of a 95% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.) [ , ] (c) What are the end points of a 99% confidence-interval estimate for the population mean? (Round to 2 digits after the decimal place.) [ , ] 7. You received a file named wage2 407.csv by email. This data file contains a sample of IID observations on wages in the target population. For this problem, round your answers to 3 digits after the decimal point. (a) Using this data file and Excel, what are the end points of a 90% confidence interval for the population mean? 2 [ , ] (b) Using this data file and Excel, what are the end points of a 95% confidence interval for the population mean? [ , ] 8. You received a file named unemp 407.csv by email. This data file contains a sample of IID observations on unemployment status in the target population. For this problem, round your answers to 3 digits after the decimal point. (a) Using this data file and Excel, what are the end points of a 90% confidence interval for the population unemployment proportion? [ , ] (b) Using this data file and Excel, what are the end points of a 95% confidence interval for the population unemployment proportion?

Answer 1

Q2) Here confidence interval is 43.8%

Alpha=1-0.438= 0.562

Zcrit= 0.58